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Evaluating polynomials over the unit disk and the unit ball

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Abstract

We investigate the use of orthonormal polynomials over the unit disk 𝔹2 in ℝ2 and the unit ball 𝔹3 in ℝ3. An efficient evaluation of an orthonormal polynomial basis is given, and it is used in evaluating general polynomials over 𝔹2 and 𝔹3. The least squares approximation of a function f on the unit disk by polynomials of a given degree is investigated, including how to write a polynomial using the orthonormal basis. Matlab codes are given.

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Correspondence to Kendall Atkinson.

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Atkinson, K., Chien, D. & Hansen, O. Evaluating polynomials over the unit disk and the unit ball. Numer Algor 67, 691–711 (2014). https://doi.org/10.1007/s11075-013-9817-5

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  • DOI: https://doi.org/10.1007/s11075-013-9817-5

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